the Elliptic Representation of a Circle, gSg 
that plane from the eye be greater than the distance of the 
picture. 
If a figure, constructed as fig. lo, happen to be inconve- 
niently large, it may be constructed upon a reduced scale. 
The triangles LOA &c. remain similar, each to itself ; whence 
the directions of the axes are the same. 
Prop. X. Prob. IV. Fig. ii. To find the same, when the 
centres are in a line parallel to the picture. 
Of the circles f, //, &c, let the centres be E, E, &c.; let 
AO and ST be a§ in Prop. IX, and D, D, the directing points 
of ST. In one circle, find the centroid V and the mean point 
M. Through these draw lines parallel to AD : which will 
cut the other lines ST in the points V and M of all. Let the 
parallel through M cut AO, or AO produced, in F. 
First case. Let AO be less * than AF. Let ii be so placed, 
that OD, being drawn, may equal DM or AF. Find G the 
directing point of the minor axis for ii ; and draw GO. 
Transfer GOA to the picture; (or place therein a similar 
triangle.) Then the minor axes, for all the circles on the 
same side of AO as ii is, are parallel to lines from points of 
GA to O ; and, the nearer any such circle is to zV, on either 
side of it, the nearer will the axis be to parallelism with GO. 
Nor is there any limit lo the approach to parallelism with GO, 
or, reversely, with AO. This, then, is a law observed. 
For the circle OM J has the shortest radius when its centre 
is at the D of ii. That radius is increased, whether M (always 
* This is always so, when the picture is perpendicular to the objective plane, if (by 
the scale) the perpendicular distance of the plane from the eye be less than the dis« 
tance of the picture; unless a mean point be between the picture and AD. 
f As LOA in prop. IX. I Drawn as in prop. VI. 
MDCCCXIV. 3 E 
